Fitting smooth paths with regularization in the sphere is an important problem in directional statistics and has important application to the estimation of apparent polar paths in paleomagnetism. This projects explores the use of Universal Differential Equations, also known as neural differential equations, to make non-parametric regression in the sphere.
We provide code for the different simulations and examples we exhibit in the project. Most of this code is provided in the Julia programming language, given that many of the libraries to perform sensitivity analysis are supported there, plus Julia solvers for differential equations are currently the state of the art in scientific computing.
This repository is organized in a way that contains most of the important elements of modern scientific workflow. We have included the following elements:
tex
: This is the folder where all the latex text belongs and what we use to compile main.pdf
.code
: Folder with both Jupyter notebooks and Julia scripts.CI
: Continuous integration with GitHub actions to automatically compile and commit the manuscript. Makefile
: make file that automatizes all the commands that can be executed within this repository.This repository has a workflow implemented that automatically compiles the latex files into the file main.pdf
and then commits this file directy to the repository.
If you are working from your fork, this action should also work and you should be able to generate the pdf file automatically using GitHub actions.
Make is an old but very useful technology that allows automation of computing processes. From the directory where you have this respository you can enter make help
from a terminal to display the different functionalities currently supported in our Makefile
. We currently support the following operations:
make tex
: Compiles the main.tex
latex file inside the folder tex
with its respective bibliografy, deletes auxiliaries files in the process and them move the generated pdf file to the home directory.This review started with some of the authors willing to understand this tools in a comprehensive way and gathering references from fields like statistics, applied mathematics and computer science. Unhappy with the lack of a general compendium of the different methods that exists to address this problem, we had decided to make a single document where all the methods can coexists under common ground and can be compareded under their different scopes and domains of applications.
We are driving by learning and undersranding and the original authors of this report decided to manage this as an open science project from the beginning. What does this entitles? Anyone interested in participating and contrubuting is welcome to join. We beleive that science will benefit for more open collaborations happening under the basis of people trying to understand a topic.
We encourage contributors to participate in this project! If you are interested in contributing, there are many ways in which you can help build this:
Issues
tab in this repository. Please explain the problem you encounter and try to give a complete description of it so we can follow up on that.Issue
in this repository, with the title of the issue being the title of the paper and adding the label paper
to the issue.The easiest way to contribute by adding code and/or text is to create a new fork of this repository and then create a pull request to the main repository. You can add changes and explore new things in your own fork of this repository and then make a pull request to the repository asking to include some of the contents in the repository. Pull requests are the best way of merging different versions of a repository since it allows to open a conversation about the new implemented changes and solve potential merge conflicts at the same time.
working from Overleaf? You can create a Overleaf project that is synchronized with a GitHub repository (see here for more information). This allows you to do edits on the text file directly from Overleaf and then push your changes directly to your fork, from where you can make a pull request to the main repository.
If you have any questions or want to reach out, feel free to send us an email to fsapienza@berkeley.edu
.